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In this case, the conjunction "OR" has a separating function rather than an enumerative one; logically, this complex sentence can be written as two simpler ones: a) the opponent cannot retreat if they have used combat magic; b) the opponent cannot retreat if they have used any other (non-combat) magic that has inflicted any damage on the opponent. Otherwise, the conjunction "AND" should have been used.
Incorrect logic. How can the conjunction "AND" be used? It would imply that two spells are cast in one round. So, the conclusion about the separating function is incorrect, especially since the rule was clearly intended to prevent the gradual elimination of the opponent's troops and their retreat, to prevent situations where, having a lot of money and a unit with high speed, one can gradually eliminate the enemy army. So, the main point of the rule is clearly magic that has inflicted any damage on the opponent.